Longitudinal Count Research Articles

Linking dynamic patterns of COVID-19 spreads in Italy with regional characteristics: a two level longitudinal modelling approach.

The current statistical modeling of coronavirus (COVID-19) spread has mainly focused on spreading patterns and forecasting of COVID-19 development; these patterns have been found to vary among locations. As the survival time of coronaviruses on surfaces depends on temperature, some researchers have explored the association of daily confirmed cases with environmental factors. Furthermore, some researchers have studied the link between daily fatality rates with regional factors such as health resources, but found no significant factors. As the spreading patterns of COVID-19 development vary a lot among locations, fitting regression models of daily confirmed cases or fatality rates directly with regional factors might not reveal important relationships. In this study, we investigate the link between regional spreading patterns of COVID-19 development in Italy and regional factors in two steps. First, we characterize regional spreading patterns of COVID-19 daily confirmed cases by a special patterned Poisson regression model for longitudinal count; the varying growth and declining patterns as well as turning points among regions in Italy have been well captured by regional regression parameters. We then associate these regional regression parameters with regional factors. The effects of regional factors on spreading patterns of COVID-19 daily confirmed cases have been effectively evaluated.

The dynamic interdependence in the demand of primary and emergency secondary care: A hidden Markov approach

This paper develops an extension of the class of finite mixture models for longitudinal count data to the bivariate case by using a trivariate reduction technique and a hidden Markov chain approach. The model allows for disentangling unobservable time-varying heterogeneity from the dynamic effect of utilisation of primary and secondary care and measuring their potential substitution effect. Three points of supports adequately describe the distribution of the latent states suggesting the existence of three profiles of low, medium and high users who shows persistency in their behaviour, but not permanence as some switch to their neighbour's profile.

The role of corporate governance in environmental policy disclosure and sustainable development. Generalized estimating equations in longitudinal count data analysis.

AbstractAddressing environmental, social, and governance (ESG) issues has become a critical element of company strategy. This study aims to investigate the relationship between corporate governance and financial characteristics and the extent of ESG disclosure in an international sample. The sample consists of 540 companies chosen from the Forbes Global 2000 list for the period 2014–2017. The econometric model used for analyzing the association between corporate characteristics and the extent of ESG disclosure is based on Generalized Estimating Equations for longitudinal count data. The current study argues that stakeholder engagement is the key to enhancing both business environmental policy and sustainable development. The statistical results show that all governance factors selected in our study, with the exception of the board size, are significant determinants that influence the extent of environmental policy disclosure.

Positivity properties of the ARFIMA[formula omitted] specifications and credibility analysis of frequency risks

Allowing for the seniority of claims and of risk exposure in the prediction of frequency risks necessitates dynamic random effects in Poisson mixtures. Non-life insurance data show evidence of long memory in stationary random effects. This paper proves that the ARFIMA(0,d,0) mixtures of Poisson distributions ensure nonnegative credibilities per period in the affine prediction of frequency risks. This is true regardless of the risk exposure. This property is maintained if the random effect is the product of a time-invariant component (which provides the highest level of memory in the data) and of a component that follows an ARFIMA(0,d,0) specification. The proof uses approximations of the ARFIMA(0,d,0) time series by AR(p) time series, which result from truncations of the filtering equations that define the former ones. Every given ARFIMA(0,d,0) specification inherits the positivity properties of the truncations because the supremum of the spectral densities of these truncations is integrable on the frequency domain. These semiparametric specifications are easily estimated from longitudinal count data, with the generalized method of moments.

An Approach to Analyze Longitudinal Zero-Inflated Microbiome Count Data Using Two-Stage Mixed Effects Models

The developments of powerful next-generation technologies provide valuable resources for investigating the human microbiome. In particular, it has been of great interest to study the longitudinal changes in the microbiome and its association with risk factors and clinical outcomes (e.g., longitudinal oral microbiome abundance and oral mucositis). The challenges of such analysis include the zero-inflated microbial abundance counts data and the correlation among the longitudinal abundance counts collected across different time points within the same patient. The current approaches for longitudinal zero-inflated microbiome abundance data focused on testing the covariate-taxon associations (i.e., time-varying abundance as the dependent variable), but ignored the taxon-outcome associations (i.e., non-time-varying clinical outcome as the dependent variable). To address this question, we proposed a two-stage mixed effects model for analyzing zero-inflated longitudinal data and the clinical outcome of interest. In this model, the longitudinal microbial abundance count data are first modeled as a function of time using the zero-inflated negative binomial mixed effects model, and at the second stage, the summaries of the temporal patterns (e.g., random intercepts and slopes) are used in the regression models (e.g., linear, accelerate failure time) to assess their associations with the outcome. Simulations showed that the two-stage mixed effects model can provide accurate estimations for the regression coefficients of the association between the longitudinal trend of microbial abundance and the outcome. We applied the proposed approach to the study of longitudinal patterns in oral microbial abundance and oral mucositis in the patients with squamous cell carcinoma of the head and neck.

Joint model for longitudinal mixture of normal and zero-inflated power series correlated responses Abbreviated title:mixture of normal and zero-inflated power series random-effects model

ABSTRACT In this paper, a joint model is presented for analyzing longitudinal continuous and count mixed responses. The frequency distribution of continuous longitudinal response variable for each subject at any time has a skewed and or multi-modal form. Then, a suitable finite mixture of normals is used as its distribution. It seems that the continuous response comes from several distinct sub-populations. The number of zeros of the count response is inflated. Also, a zero-inflated power series (ZIPS) distribution is applied as its distribution in order to model the count response. The correlation of longitudinal responses through time and that of mixed continuous and count responses are modeled by utilizing the random-effects vectors in the finite mixtures of regression (FMR) models. Further, a full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. Then, some simulation studies are performed for assessing the performance of the model. Additionally, an application is illustrated for joint analysis of the number of days during the last month that the individual drank alcohol, as well as the respondents’ weight. Finally, the two first times of the Americans Changing Lives survey are evaluated.

Supplemental Material for Analyzing Discontinuities in Longitudinal Count Data: A Multilevel Generalized Linear Mixed Model

Supplemental Material for Analyzing Discontinuities in Longitudinal Count Data: A Multilevel Generalized Linear Mixed Model

Marginal models for longitudinal count data with dropouts

In this article, we investigate marginal models for analyzing incomplete longitudinal count data with dropouts. Specifically, we explore commonly used generalized estimating equations and weighted generalized estimating equations for fitting log-linear models to count data in the presence of monotone missing responses. A series of simulations were carried out to examine the finite-sample properties of the estimators in the presence of both correctly specified and misspecified dropout mechanisms. An application is provided using actual longitudinal survey data from the Health and Retirement Study (HRS) (HRS, 2019)

Efficient and Accurate Inference of Mixed Microbial Population Trajectories from Longitudinal Count Data.

The recently completed second phase of the Human Microbiome Project has highlighted the relationship between dynamic changes in the microbiome and disease, motivating new microbiome study designs based on longitudinal sampling. Yet, analysis of such data is hindered by presence of technical noise, high dimensionality, and data sparsity. Here, we introduce LUMINATE (longitudinal microbiome inference and zero detection), a fast and accurate method for inferring relative abundances from noisy read count data. We demonstrate that LUMINATE is orders of magnitude faster than current approaches, with better or similar accuracy. We further show that LUMINATE can accurately distinguish biological zeros, when a taxon is absent from the community, from technical zeros, when a taxon is below the detection threshold. We conclude by demonstrating the utility of LUMINATE on a real dataset, showing that LUMINATE smooths trajectories observed from noisy data. LUMINATE is freely available from https://github.com/tyjo/luminate.

Competing risks joint models using R-INLA

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

Analysis of joint modeling of longitudinal zero-inflated power series and zero-inflated time to event data

ABSTRACT In longitudinal studies measurements are often collected on different types of responses for each individual. These may contain several longitudinally measured responses (such as the CD4 count) and the time at which an event occurs (e.g., HIV, death, or dropout from the study). These outcomes are often separately analyzed. Compared to separate modeling, joint modeling and simultaneous analysis allows for more coherent, robust analysis and may produce a better insight into the process under study. However, there has always been difficulty to the analyst that finding a proper multi-variable joint distribution for linking responses. In this article, we survey the zero-inflated property for longitudinal count and time to event data. We apply a member of the family of power series distributions (PSDs) and the Cox proportional hazard regression model (Cox PH) with Weibull baseline hazard rate, respectively, for these correlated responses. Also we consider both right and left censoring mechanisms in time to event process. This modeling strategy leads to expand the class of joint models and presents some new joint models which, as far as we know, have not yet been investigated by other researchers. The parameters in the joint model are estimated by using likelihood techniques.

Joint modelling of longitudinal and time-to-event data: an illustration using CD4 count and mortality in a cohort of patients initiated on antiretroviral therapy

BackgroundModelling of longitudinal biomarkers and time-to-event data are important to monitor disease progression. However, these two variables are traditionally analyzed separately or time-varying Cox models are used. The former strategy fails to recognize the shared random-effects from the two processes while the latter assumes that longitudinal biomarkers are exogenous covariates, resulting in inefficient or biased estimates for the time-to-event model. Therefore, we used joint modelling for longitudinal and time-to-event data to assess the effect of longitudinal CD4 count on mortality.MethodsWe studied 4014 patients from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) who initiated ART between June 2004 and August 2013. We used proportional hazards regression model to assess the effect of baseline characteristics (excluding CD4 count) on mortality, and linear mixed effect models to evaluate the effect of baseline characteristics on the CD4 count evolution over time. Thereafter, the two analytical approaches were amalgamated to form an advanced joint model for studying the effect of longitudinal CD4 count on mortality. To illustrate the virtues of the joint model, the results from the joint model were compared to those from the time-varying Cox model.ResultsUsing joint modelling, we found that lower CD4 count over time was associated with a 1.3-fold increase in the risk of death, (HR: 1.34, 95% CI: 1.27-1.42). Whereas, results from the time-varying Cox model showed lower CD4 count over time was associated with a 1.2-fold increase in the risk of death, (HR: 1.17, 95% CI: 1.12-1.23).ConclusionsJoint modelling enabled the assessment of the effect of longitudinal CD4 count on mortality while correcting for shared random effects between longitudinal and time-to-event models. In the era of universal test and treat, the evaluation of CD4 count is still crucial for guiding the initiation and discontinuation of opportunistic infections prophylaxis and assessment of late presenting patients. CD4 count can also be used when immunological failure is suspected as we have shown that it is associated with mortality.

Gaussian copula joint models to analysis mixed correlated longitudinal count and continuous responses

Gaussian Copula joint models for analyzing mixed correlated longitudinal continuous and count responses with random effects are presented where the count response is defined by a latent variable approach, and its distribution is a member of the power series family of distributions. A copula-based joint model is proposed that accounts for associations between count and continuous responses. A full likelihood-based inference method for estimation is used by which maximum likelihood estimation of parameters is obtained. To illustrate the utility of the models, some simulation studies are performed. Finally, the proposed models are motivated by analyzing a medical data set where the correlated responses are the number of joint damaged obtained from the severity of osteoporosis (count response) and Body Mass Index (continuous response). Effects of some covariates on responses are investigated simultaneously. Besides, identifiability of parameters, detection of outlines by examining residuals and sensitivity analyses are fully investigated.

A robust Bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete Weibull distribution.

This article proposes a Bayesian mixed effects zero inflated discrete Weibull (ZIDW) regression model for zero inflated and highly skewed longitudinal count data, as an alternative to mixed effects regression models that are based on the negative binomial, zero inflated negative binomial, and conventional discrete Weibull (DW) distributions. The mixed effects ZIDW regression model is an extension of a recently introduced model based on the DW distribution and uses the log-link function to specify the relationship between the linear predictors and the median counts. The ZIDW approach offers a more robust characteristic of central tendency, compared to the mean count, when there is skewness in the data. A matrix generalized half-t (MGH-t) prior distribution is specified for the random effects covariance matrix as an alternative to the widely used Wishart prior distribution. The methodology is applied to a longitudinal dataset from an epilepsy clinical trial. In a data contamination simulation study, we show that the mixed effect ZIDW regression model is more robust than the competing mixed effects regression models when the data contain excess zeros or outliers. The performance of the ZIDW regression model is also assessed in a simulation study under the specification of, respectively, the MGH-t and Wishart prior distributions for the random effects covariance matrix. It turns out that the highest posterior density intervals under the MGH-t prior for the fixed effects maintain nominal coverage when the true variability between random slopes over time is small, whereas those under the Wishart prior are generally conservative.

Progression of HIV Disease Among Patients on ART in Ethiopia: Application of Longitudinal Count Models.

Although the world has been fighting HIV disease in unity and patients are getting antiretroviral therapy treatment, HIV disease continues to be a serious health issue for some parts of the world. A large number of AIDS-related deaths and co-morbidities are registered every year in resource-limited countries like Ethiopia. Most studies that have assessed the progression of the disease have used models that required a continuous response. The main objective of this study was to make use of appropriate statistical models to analyze routinely collected HIV data and identify risk factors associated with the progression of the CD4+ cell count of patients under ART treatment in Debre Markos Referral Hospital, Ethiopia. In this longitudinal retrospective study, routine data of 445 HIV patients registered for ART treatment in the Hospital were used. As overdispersion was detected in the data, and Poisson-Gamma, Poisson-Normal, and Poisson-Gamma-Normal models were applied to account for overdispersion and correlation in the data. The Poisson-Gamma-Normal model with a random intercept was selected as the best model to fit the data. The findings of the study revealed the time on treatment, sex of patients, baseline WHO stage, and baseline CD4+ cell count as significant factors for the progression of the CD4+ cell count.

Application of the Poisson-Tweedie distribution in analyzing crash frequency data

This paper describes a study that applies the Poisson-Tweedie distribution in developing crash frequency models. The Poisson-Tweedie distribution offers a unified framework to model overdispersed, underdispersed, zero-inflated, spatial, and longitudinal count data, as well as multiple response variables of similar or mixed types. The form of its variance function is simple, and can be specified as the mean added to the product of dispersion and mean raised to the power P. The flexibility of the Poisson-Tweedie distribution lies in the domain of P, which includes positive real number values. Special cases of the Poisson-Tweedie distribution models include the linear form of the negative binomial (NB1) model with P equal to 1.0, the geometric Poisson (GeoP) model with P equal to 1.5, the quadratic form of the negative binomial (NB2) model with P equal to 2.0, and the Poisson Inverse Gaussian (PIG) model with P equal to 3.0. A series of models were developed in this study using the Poisson-Tweedie distribution without any restrictions on the value of the power parameter as well as with specific values of the power parameter representing NB1, GeoP, NB2, and PIG models. The effects of fixed and varying dispersion parameters (i.e., dispersion as a function of covariates) on the variance and expected crash frequency estimates were also examined. Three years (2012–2014) of crash data from urban three-leg stop-controlled intersections and urban four-leg signalized intersections in the state of Florida were used to develop the models. The Poisson-Tweedie models or the GeoP models were found to perform better when the dispersion parameter was constant or fixed. With the varying dispersion parameter, the NB2 and PIG models were found to perform better, with both performing equally well. Also, the fixed dispersion parameter values were found to be smaller in the models with a higher value of the power parameter. The variation across the models in their estimates of weight factor, expected crash frequency, and potential for safety improvement of hazardous sites based on the empirical Bayes method was also discussed.

Generalized Quasilikelihood Inference for Zero Inflated Longitudinal Count Data

In this paper, we extend an observation-driven model for time series of zero inflated count data to longitudinal data setup. Basic properties of the models are discussed. For statistical inference of the proposed model, a generalized quasilikelihood (GQL) estimating equation has been derived for the regression parameter. A pharmaceutical data has been reanalyzed using the proposed approach and results are compared. The proposed approach produces similar estimates as given in the earlier work with much smaller standard errors.
 Dhaka Univ. J. Sci. 68(1): 95-99, 2020 (January)

Longitudinal Count Data Analysis of Factors Affecting Epileptic Seizure of Patients in Case of Gondar Referral Hospital, Northwest Ethiopia

Even though the world is fighting epileptic seizure disease in unity and patients are getting treatment, it continued to be a serious health issue for parts of the world and a large number of patients are being registered every year. The main objective of this study was to identify associated risk factors affecting the progression of patients in Gondar Referral Hospital. In this longitudinal count data analysis, data was collected from 337 epileptic seizure patients registered for treatment from January 1, 2016 to April 30, 2018 in the Hospital and Poisson, Poisson-gamma, Poisson-Normal and Poisson-Gamma-Normal models were applied to the data. Poisson-Gamma-Normal model with random intercept was selected as a best model to fit the data based on different model selection criteria. The findings of the study revealed that time, brain injury, treatment, interaction of time with residence and interaction of time with brain injury were significant factors for epileptic seizure of the patients. Minimization of epileptic seizure of patients in response to treatment was observed, which means the patients were at decreased epileptic seizure when enrolled for treatment. Therefore, patients should be encouraged to stay on treatment.

"Modelling Zero-inflated Bivariate Count Responses using Marginal-Conditional Approach with application to Traffic Accidents and Fatalities Data"

Zero-inflated bivariate count responses frequently occur in medical, environmental, ecological, social and transportation studies. These bivariate count responses recorded from a group of independent subjects or from a specific time or place may suffer the presence of excessive zeros, so constitute complexity while modelling. Although the responses under the umbrella of zero-inflated clustered and longitudinal count setup have been studied extensively in the past two decades, the literature is rather limited for analyzing zero-heavy bivariate count data. In this paper, we propose a marginal-conditional approach based bivariate zero-inflated Poisson-Poisson regression model to overcome the complexity imposed due to excessive zeros in bivariate count responses.

A new Bayesian joint model for longitudinal count data with many zeros, intermittent missingness, and dropout with applications to HIV prevention trials

In longitudinal clinical trials, it is common that subjects may permanently withdraw from the study (dropout), or return to the study after missing one or more visits (intermittent missingness). It is also routinely encountered in HIV prevention clinical trials that there is a large proportion of zeros in count response data. In this paper, a sequential multinomial model is adopted for dropout and subsequently a conditional model is constructed for intermittent missingness. The new model captures the complex structure of missingness and incorporates dropout and intermittent missingness simultaneously. The model also allows us to easily compute the predictive probabilities of different missing data patterns. A zero-inflated Poisson mixed-effects regression model is assumed for the longitudinal count response data. We also propose an approach to assess the overall treatment effects under the zero-inflated Poisson model. We further show that the joint posterior distribution is improper if uniform priors are specified for the regression coefficients under the proposed model. Variations of the g-prior, Jeffreys prior, and maximally dispersed normal prior are thus established as remedies for the improper posterior distribution. An efficient Gibbs sampling algorithm is developed using a hierarchical centering technique. A modified logarithm of the pseudomarginal likelihood and a concordance based area under the curve criterion are used to compare the models under different missing data mechanisms. We then conduct an extensive simulation study to investigate the empirical performance of the proposed methods and further illustrate the methods using real data from an HIV prevention clinical trial.